Points R and S are two points on the surface on a latitude 48°S. The two points lie on longitudes 34°W and 146°E respectively. By taking the earth’s…
Points R and S are two points on the surface on a latitude 48°S. The two points lie on longitudes 34°W and 146°E respectively. By taking the earth’s radius to be 6370km, calculate the distance from R to S along a parallel of latitude. (Take π = 22/7)
[sin 48° = 0.7431, cos 48° = 0.6691, tan 48° = 1.1106]
[sin 34° = 0.5592, cos 34° = 0.8290, tan 34° = 0.6745]
[sin 146° = 0.5592, cos 146° = -0.8290, tan 146° = -0.6745]
Both points are on latitude 48°S. One is 34°W and the other is 146°E. The angle between them along the parallel is 34° + 146° = 180°.
The radius of the parallel of latitude is R cos 48° = 6370 × 0.6691 ≈ 4262 km.
Distance = (180/360) × 2π × 4262 = π × 4262 = 22/7 × 6370 × 0.6691 ≈ 13,395 km. The nearest option is 13,396 km.
Using the earth’s full radius 6370 km instead of R cos 48° would be wrong, because the path follows a parallel, not the equator.
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